Chapter 1 - Limits and Continuity - 1.1 Limits (An Intuitive Approach) - Exercises Set 1.1 - Page 60: 19

False

A limit "existing" simply means that it has a non-infinity value. It could be the case that $\lim\limits_{x \to a^{+}} = -1$ and $\lim\limits_{x \to a^{-}} = 0$ (for example, $x=0$ in Figure Ex-10). These two half-limits both exist, but since they are not equal, the two sides do not 'join up' and the full limit does not exist.